I tested this solution on both my 3Ds XL and my regular 3Ds. It's fully functional but it requires some work.
To circumvent the problem with public access WiFi, like SecondCup, McDonalds WiFi, aka "your local guest connection", you need two things:
1. A working mobile device, any type will do, Apple, Android, Windows operating systems respectively.
2. An application on the device that can obtain your Internet IP configuration settings. (Example: ipconfig for Android phones and tablets.)
Process:
A) Assuming you've got the required stuff, start by clearing the browser history and saved cookies on your 3Ds browser as this can interfere with the process.
If it is a home - guest signal, also be sure to reset the modem first.
B) Access the authentication page of the WiFi signal you're trying to connect to with your mobile phone, tablet, etc. And write down the page address.
C) Next, open up your 3Ds system settings and begin making a new internet connection.
D) All of the connection has to be created manually, beginning with the WiFi connection name which is the SSID. Security type = none, don't enter anything there.
E) Next enter the IP address from the configuration app on your mobile device, followed by the Subnet Mask and Gateway it shows.
After saving that part the 3Ds will ask you to set up the DNS, enter 8.8.8.8 into the top setting where it asks for it, leave the bottom blank. Save the setting, Do Not Test the connection.
F) Once back into the main 3Ds screen, wait for the Internet signal to switch to solid blue, open the browser, enter the authentication page address you got from your mobile device, accept terms and conditions or enter whatever authentication info is needed.
H) Enter the system settings once again, go into the Connection Setting you initially created, set its IP and DNS info to automatic now and save. Again, Do Not Test the connection.
I) Go back to the browser, re-accept the terms and conditions page. It's smooth sailing from here.
Happy Connecting!
The easier thing to do is buy an old DS lite browser cartridge.